Wind Turbines Flashcards
What is the equation for power of wind blowing through an area?
P = 1/2 ρ A v^3
What are the wind industry roughness classes?
0 - Water
0.5 - Flat land
1 - Agri-land with shallow hills
2 - Agri-land with Buildings
3 - Forest/Towns
4 - Cities
What is the roughness length for class 0? What about for class 4?
0: z0 = 0.0002m
4: z0 = 1.6m
What is the condition of a Weibull Distribution that causes it to be referred to as Rayleigh Distribution?
β = 2
What does a Weibull Distribution represent?
The number of hours per year of each wind speed
Where is there viscous flow around an aerofoil?
In the thin boundary layer
How do pressure and shear stress act relative to the surface of an aerofoil?
Pressure is normal
Shear stress is tangential
How are lift and drag defined in terms of the resultant force and freestream wind velocity?
Lift is the component of resultant perpendicular to velocity, Drag is parallel component
Which surface of an aerofoil experiences suction resulting in lift?
The upper surface where velocity is higher
What causes stall of an aerofoil?
Angle of attack increases to the extent that flow detaches from the upper surface
Why are aircraft aerofoils unsuitable for wind turbines?
They are used at a lower Reynolds number than ideal
They are thicker than necessary for turbines
What does the actuator disk model assume?
No mixing of air from adjacent turbines
Air is inviscid and incompressible
Total pressure is constant before and after the disk but not through it
What is the equation for air velocity downstream of a wind turbine?
Uw = (1-2a)U∞ where U∞ is upstream velocity and a is axial flow induction factor
What is the axial flow induction factor?
1 minus the ratio of pressure at the disk to pressure upstream
What are the coefficients of power and thrust relative to axial flow induction factor a?
Cp = 4a(1-a)^2
Ct = 4a(1-a)
What changes about the flow as it passes through the actuator disk?
It loses streamwise velocity
It gains rotation
Why are actuator disk models used?
Simple
Low cost
Accurate
What is the difference between angle of attack (α) and pitch (β)
Angle of attack is between the aerofoil centreline and the angle of wind approach
Pitch is between centreline and reference plane (horizontal vertical etc)
What is the equation for flow angle Φ?
Φ = atan ((1-a)/(1+a’)LSR))
How can the power generated by a wind turbine be expressed most simply?
Torque multiplied by rotational velocity of blades
What is the equation for tangential induction factor a’?
(a(1-a))/(LSR)^2
How do chord and twist typically vary along a turbine blade?
They decrease exponentially with radius down the blade
What do the provided chord and twist equations assume?
Drag is negligible
How is a linear taper blade designed?
A chord distribution is chosen which is tangential to the ideal distribution at a specified point
Why are linear taper designs used?
They are more cost-effective to design and build
What are the limitations of BEMT?
Doesn’t account for tip losses
Has to assume a is uniform along the blade
What is the LSR with no tip losses?
TSR * r/R
What is the BEMT equation for iterating phi?
phi = atan [(1-a)/((1+a’)LSR)]
What is the equation for S in the BEMT equations?
cot phi (aka. 1/tan phi)
For the sake of simplifying the BEMT we can define a term X. What is X?
sqrt(1+S^2)
How is alpha obtained for Cl(alpha) and Cd(alpha)?
alpha = phi - ideal twist angle ‘beta’
Both of the BEMT equations give their solutions as fractions. How are the fractions different for a and a’?
For a the denominator is 1-a, for a’ it is 1+a’. Both have the respective a as the numerator
What term, Y, precedes both BEMT equations?
Bc/(8pi r) where c is chord distribution
Using the simplifications X and Y, what is the BEMT equation for a?
Y * X * (ClS + Cd)
Using the simplifications X and Y, what is the BEMT equation for a’?
Y * X/S * (Cl - CdS)
What is the actuator disk model?
A representation of a turbine as a 1D disk with swept area Ad
